Finite Group Databasebeta

C2×#360×D47 #26369213

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#360×D47

Splittings

FittingC2×C47×#360 ⋊ C2
SylowC47 ⋊ C22×#360

Subgroups

subgroupG/H
centerC22#102×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#360C2
socleC22×C47C2×#102
prime radicalC2×#135×D47C2
cosocleC2×C8×C47C24
hypercenterC2×#360D47
hypocenterC47C22×#360
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322503);